Circle left or right. Circling involves all the dancers holding hands and moving in a circular rotation to the left or the right, depending on what the caller tells them to do. Circling is not a step that requires an even number of dancers, so it works with three people.
Move forward and back. After you circle to the left or to the right, the three dancers can keep their hands joined and move forward three steps towards the center of the circle, and back three steps away from the circle.
Swing the dancers, two at a time. With three people, you cannot all swing at once. One person will stand by while the other two form a pair by linking arms, and skipping around in a circle. One of the dancers will unlink arms and join the third person, who was standing by, so they can swing together. While the person stands by, he can clap his hands to the music.
Promenade single file. A promenade is a walk around the circle and is often performed by couples but can also be done individually. Perform the promenade individually so the couples are not uneven.
Improvise your steps. During the breaks that the caller calls, come up with your own moves on the dance floor that fit the square dancing theme, but that also work for a group of three. As long as you keep up with the rhythm of the music, you can improvise the steps.